A Lattice Boltzmann Model of Binary-Fluid Mixtures

Abstract

We introduce a lattice Boltzmann model for simulating an immiscible binary fluid mixture. Our collision rules are derived from a macroscopic thermodynamic description of the fluid in a way motivated by the Cahn-Hilliard approach to non-equilibrium dynamics and ensure that a thermodynamically consistent state is reached in equilibrium. The non-equilibrium dynamics is investigated numerically and found to agree with simple analytic predictions in both the one-phase and the two-phase region of the phase diagram. PACS numbers: 02.70Ns, 64.90.+b, 47.11.+j 1 Since the introduction of automaton based models capable of simulating hydrodynamic phenomena [1], lattice gas and lattice Boltzmann techniques have proved to be extremely useful numerical tools for investigating fluid dynamics. These approaches have been applied to a variety of different physical problems ranging from the simple flow of one componentfluids to multi-component fluid dynamics in random porous media [2], a problem of great interest to the oil industry [3].